The King's Chessboard Rachel Cohen

The King's Chessboard
By David Birch

1. Long ago in India, there lived a king and a wise man. The king wanted to reward the wiseman. The two fought about a reward because the wise man felt he didn't deserve or want one. Finally, the wise man noticed the king's chessboard. He said to the king, "Tomorrow, for the first square of your chessboard give me one grain of rice, the next day, for the next square two grains of rice, and the next day four grains," and so on. And so for every square of the chessboard, the amount of grains is doubled from the previous day. 

The king was curious how much rice it would amount to in total because there were 64 squares on the chessboard. He didn't say anything, however, so as not to make himself look like a simpleton. Then the king granted the wise man's request. The king sent a servant dressed in the best manner possible to deliver the first grain. The wise man simply thanked him and placed the grain on his chessboard. The king heard this, and placed a single grain on his chessboard. This went on and on. The wise man would place a single grain of rice on his board and give the rest away.

The counting of grains became too much for the king's weigher, so he began to simply weigh the rice, beginning with one ounce. The weigher grew concerned with the amounts of rice being given to the wise man and tried to warn the king's advisor, but it backfired. 

A few days later, the advisor saw four grainery workers carry sacks of rice and asked where they were taking it. One of them responded that it was going to the wise man who then distributed it to the poor and the needy. The advisor felt that the weigher had made a mistake, but it was explained to him how the amounts grew and grew, doubling each day. 

After a few days, the king saw sixteen wagons carrying over a ton of rice each and heard people cheering. He demanded to know where the rice was going. The advisor explained to him that the rice was for the wise man and that despite it seeming impossible, there had been no mistake, the math was all correct. 

The king then asked for his mathematicians so as do determine how many pounds of rice he had promised the wise man. At seeing the toal number the king became angry. 549, 755, 830, 887 tons of rice were to be given to the wise man. 

The queen then insisted that the king ask the wise man to be released of the agreement. The king ignored her, but the next day, the thirty-second day, he summoned the wise man. The king told him that there wasn't enough rice in India to fulfill the promise. the wise man agreed that there wasn't even enough in the whole world. 

The king demanded another way to satisfy the wise man, but the wise man responded that he had always been satisfied. The wise man argued that it is the king who must be satisfied, not the wise man. The king said he was satisfied and that he understood that the wise man had taught him an important lesson. 

The wise man served the king many more times, but never again was he asked about how he could be repaid. The king kept the chessboard for the rest of his life, to remind him "how easy it is for pride to make a fool of anyone, even a king."  

2. The King's Chessboard explains exponential growth in the form of a folk tale, using grains of rice to show how rapidly exponential growth occurs. 1 grain on the first day, 2 on the second, 4 on the third, 8 on the fourth, 16 on the fifth, 32 on the sixth. On the eleventh day, the switched to ounces, which after five days grew to pounds. On the fifteenth day,16 pounds. On the twentieth day 1512 pounds. On the twenty-fifth day 16,384 pounds. And on and on increasing exponentially until what would have been the sixty-fourth day. This exponential growth can be expressed as 2^n, where n is greater than or equal to zero. This fable is an effective and engaging way of explaining a somewhat complicated mathematical concept in simple terms. 

3. Literature is a good way of explaining mathematical concepts because it literally spells out what is happening in the mathematical concepts in everyday terms. By providing a background story or anecdote, the concept is given a context and real life expression, allowing for it to be more easily digested.